Lesson 3

Equations for Functions

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Here is an equation that represents a function: $$72x+12y=60$$.

Select all the different equations that describe the same function:

A:

$120y + 720x = 600$

B:

$y = 5 - 6x$

C:

$2y + 12x = 10$

D:

$y = 5 + 6x$

E:

$x=\frac{5}{6} - \frac{y}{6}$

F:

$7x + 2y = 6$

G:

$x=\frac{5}{6} + \frac{y}{6}$

Problem 2

1. Graph a system of linear equations with no solutions.
2. Write an equation for each line you graph.
(From Grade8, Unit 4, Lesson 13.)

Problem 3

Brown rice costs \$2 per pound, and beans cost \$1.60 per pound. Lin has \\$10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let $$b$$ be the number of pounds of beans Lin buys and $$r$$ be the number of pounds of rice she buys when she spends all her money on this meal.

1. Write an equation relating the two variables.
2. Rearrange the equation so $$b$$ is the independent variable.
3. Rearrange the equation so $$r$$ is the independent variable.

Problem 4

$$2x+4(3-2x)=\frac{3(2x+2)}{6}+4$$
$$4z+5=\text-3z-8$$
$$\frac12-\frac18q=\frac{q-1}{4}$$